If f(1) = 10 and f '(x) ≥ 3 for 1 ≤ x ≤ 6, how small can f(6) possibly be?

Answers

Answer 1

Answer:

[tex]f'( x ) = \frac{f(b) - f(a)}{b - a} \\ = \frac{f(6) -f(a)}{6 - 1} \\ 3\leqslant \frac{f(6) - 10}{5} \\ 15\leqslant f(6) - 10 \\ f(6) \geqslant 15 + 10 \\ f(6) \geqslant 25[/tex]

Answer 2

Answer:

25

Step-by-step explanation:

Our "best" case is when [tex]f'(x) = 3[/tex] everywhere - if it changes it means [tex]f(x)[/tex] will grow faster. But if [tex]f'(x)[/tex] is constant, it means [tex]f(x)[/tex] is the straight line [tex] y-10 = 3 (x-1) [tex], which passes through the point (6, 25)


Related Questions

Question 1:
Write the specific equation for the kinetic energy E (measured
in Joules) of an 1100-kg car. Use this equation to compare the kinetic
energy of an 1100-kg car moving at a velocity of 10 meters per second to
the kinetic energy of the same car moving at 3 times the velocity.

Answers

Answer:

Step-by-step explanation:

KE = ½mv²

KE₁₀ = ½(1100)10² = 55000 = 55 kJ

KE₃₀ = ½(1100)30² = 495000 = 495 kJ

9 times greater

Your business requests a 3-month loan for
$500,000. What will be the interest paid at the
end of the term if the business risk percentage is
assessed at 2.0% and LIBOR is at 2.1%?
interest paid = $ [?]
=
Round to the nearest hundredth.
Entor

Answers

Answer:

im preety sure its 561500

Step-by-step explanation:

4.1% x 4 is 61500 + 500000 = 561500

Which statement is true about the expressions below?

Answers

Is there a attachment because I don’t see anything

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs ​$69. A season ski pass costs ​$350. The skier would have to rent skis with either pass for ​$25 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily​ passes? The skier would have to go skiing nothing days. plz answer right and give more info on how u got the answer ty

Answers

Divide the season pass cost by the daily capstone:

350 / 69 = 5.07

They would have to ski 6 days for the season pass to be less expensive

solve for completing the square x^2-12x+11=0

Answers

Answer:

x = 6 ± 5

Step-by-step explanation:

x² - 12x + 11 =0

x² - 12x = -11          Now add this number to both sides of the equal sign (1/2 of the coefficient of x-term squared)

x² - 12x +36 = -11 + 36                      1/2(-12)² = 36

(x - 6)(x - 6) = 25

(x - 6)² = 25

[tex]\sqrt{(x-6)}[/tex]² = [tex]\sqrt{25}[/tex]                             square root of both side of the equation

x - 6 =  ± 5                                          (5)² = 25 and (-5)² = 25

x = 6 ± 5

Can someone please hurry and finish this question please!!!! Will give brainliest

Answers

Answer:

2b. R line is lower.

2c. It is lower because the y-intercept is negative.

Answer: ill take one for you john

Step-by-step explanation:

Multiply.


[−8 ⋅ 4/11] ⋅ [(−0.1) ⋅ 22]


What is the product?


pls help!!!

Answers

The answer is 6.4
Fraction form: 32/5

Nick will apply for a business loan for his toy company. The loan officer asked Nick to determine the
company's current value and growth for the next few years. Nick projected a steady growth rate for his
toy business.

Is Nick's model linear or exponential? How do you
know?

Year Project Value
0 $25,000.00
1 $26,250.00
2 $27,562.50
3 $28,940.63
4 $30,387.66
5 $31,907.04

PLEASE HELP ME ✔️

Answers

Answer:

Dividing the current value by the previous value ALWAYS equals 1.05.

Since the growth rate is constant, it is linear.

Step-by-step explanation:

Answer:

Exponential

Step-by-step explanation:

The relationship is linear when the rate of change is constant. It means the sequence of the dependent variable forms an arithmetic sequence.

We see the the sequence of Projected Value is not arithmetic but geometric sequence with common ratio of 1.05.

It will have equation:

y = 25000*1.05ˣ

This is therefore exponential.

Helppppppp plzzzzzzz

Answers

Answer:

102°

Step-by-step explanation:

Angles in a straight line is added up to 180°

So,

Angle 1 + Angle 2 = 180°

Given that,

Angle 2 = 78°

We can find angle 1

Let us find,

Let the angle 1 be x

[tex]x+78=180\\x=180-78\\x=102[/tex]

As a and b lines are parallel,

Angle 1 = Angle 5 (Corresponding angles)

Also we already found the angle 1

So,

Angle 5 = 102°

Hope this helps you.

Let me know if you have any other questions :-)

Can someone help answering my questions in English and Math

Answers

Answer:

yo

Step-by-step explanation:

solve pls brainliest

Answers

Answer:

For the first question, it's the third line, the second one after zero.

For the second question, it's the 7th line in total, the 6th one after zero.

Step-by-step explanation:

please help ME I BEG YOU​

Answers

Step-by-step explanation:

I think it is 44.

if wrong forgive me.

hope this helps.

Answer:

44

Step-by-step explanation:

1. To round a number to the nearest 10, look at the ones-digit. If the digit is 5 or more, round up (raise the score). If the digit is 4 or less, round down (let it rest).

2. The ones-digit in 44 is 4 or less, meaning we round down. The 4 in the ones-place becomes zero, and therefore, rounds to 40.

Therefore, the answer is 44.

Which angles are corresponding angles?

Answers

Answer:

OPN and QPS are corresponding angles

< OPN and < RSP are corresponding angles.


Corresponding angles are two angles that are on the same side of the transversal, one an interior angle (between the lines), the other an exterior angle that were not adjacent.

< OPN is the exterior angle, and < RSP is the interior angle.

what is rhe vertex of the graph of the function f(x)=x²+6x+9​

Answers

what is rhe vertex of the graph of the function f(x)=x²+6x+9

Find the Area of the figure below, composed of a parallelogram and one semicircle. Rounded to the nearest tenths place


Answers

Hi,

Recall that the area of a parallelogram is the product of the base b and the height or "altitude" h. So the formula is : b * h. b = 20 here, and h = 6, so we get : 20 * 6 = 120.

Now we have to compute the area of the semicircle, remember the formula for the area of a circle is : πr² where r is the radius of the circle. If we watch the figure, we already have the value of the diameter d = 8. So the radius is equal to half the diameter : r = 8 /2 = 4

Now applying the formula we get : πr² = π * 4² ≈ 50.3 rounded to the nearest tenth place.

But we don't wont the area of the circle, we want half the area of it, since it's a semicircle : πr² / 2 ≈ 25.1 rounded to the nearest tenth place.

Now to get the whole area of the figure, we need to sum the area of the parallelogram with the area of the semicircle : 120 + 25.1 ≈ 145.1 rounded to the nearest tenth place.

Good Luck

Simplify the following integer exponents:​

Answers

For question 1 simplifying integer exponents :
1) 729
2) 1/625
3)1

can anyone heelp me pls

Answers

Answer:

lotion 3,. suspension 2, capsule 1 , I think

I need a lil help here (18 points!!!!!)

Answers

Answer:

correct answer is 2

............................

Answer U4

Step-by-step explanation:

blank is 4

yall what is this? I dont really know what to do

Answers

Answer:

you did it right

Step-by-step explanation:

Tbh you were actually correct

ok this is stressin me out anyone know this

Answers

X=7.
9x-7y=63
9x-7 x 0=63
9x - 0=63
9x=63
X=7.

Y=-9
9 x 0 -7y=63

Was the HOA president right for doing so? What other factors could have contributed to both the rise in ice cream sales and murders? Is this an example of correlation or causation?

Answers

Answer:

No, the HOA president was wrong because both murder and ice cream sales spiked during the summer months but slowly decreased during months in the spring, fall and winter times. This is an example of causation.

Step-by-step explanation:

I wouldn't put exactly that because i put that on mine but here's an idea!

Hope this helps! <3

Have a nice day/night!

Order the expressions by choosing >,<, or =

Answers

Answer:

1. <

2. <

3. >

Step-by-step explanation:

Remember in order to solve exponents you need to multiply the whole number by itself as many times as it's exponent so if you have 3^4 you need to multiply three by itself four times.

1. [tex]2^5 = 2\times2\times2\times2\times2[/tex]

[tex]2\times2\times2\times2\times2=32[/tex]

[tex]=32[/tex]

[tex]2^2 = 2\times2[/tex]

[tex]2\times2=4[/tex]

[tex]32\times4=128[/tex]

[tex]2^{10} = 2\times2\times2\times2\times2\times2\times2\times2\2\times2\times2[/tex]

[tex]2\times2\times2\times2\times2\times2\times2\times2\2\times2\times2=1024[/tex]

128 < 1024

2. [tex]2^2=2\times2=4[/tex]

[tex]5^2=5\times5=25[/tex]

[tex]4\times25=100[/tex]

[tex]=100[/tex]

[tex]2^{10} = 1024[/tex]

100 < 1024

3. [tex]2^5 = 32[/tex]

[tex]5^2=25[/tex]

[tex]32\times25=800[/tex]

[tex]10^2 = 10\times10 = 100[/tex]

800 > 100

Hope this helps.

This​ week, 951 people went to the beach. Last​ week, 1,173 people went to the beach. The number of people who went to the beach fell by what​ percent?
HELP ME PLS

Answers

It fell by 19%
Use 1173 as your total and then find the percent from 951 and subtract from 100 and that’s the percent that fell

What is the y-intercept for the equation 4x+2y=6?

Answers

Answer:

The y intercept is 3

(0,3)

Step-by-step explanation:

4x+2y=6

To find the y intercept, set x =0 and solve for y

4(0) +2y = 6

0+2y = 6

Divide by 2

2y/2 = 6/2

y =3

The y intercept is 3

(0,3)

NO LINKS!!! Part 1: y = x^3

Shape:
Domain:
Range:
Locater point:​

Answers

Answer:

Shape: Not sure what to put

Domain: ( -oo, oo )

Range: ( -oo, oo )

Locater point: ( 0, 0 )

Step-by-step explanation:

Shape - You have the shape on the graph

Domain and Range - Both go on forever since there is no hole/interruption

Locater Point: I would say origin because it is the closest thing to a vertex, which is an example of a locater point.

Hopefully this helps!

Brainliest please?

If A = {1, 4, 5, 6, 7}, B={1, 2, 5, 8, 9} and C={3, 4, 5}
Then find A∪ B ∪ C

Answers

Answer:

A U B U C = {1,2,3,4,5,6,7,8,9}

Step-by-step explanation:

This is the correct form

Answer:

A={1,4,5,6,7}

B={1,2,5,8,9}

C={3,4,5}

AUBUC= all elements of A,B,C

={1,2,3,4,5,6,7,8,9}

What ratio is equivalent to 9:6 ?

12:8
7:4
3:1
15:10

Answers

Answer:

15:10

Step-by-step explanation:

15:10 can be reduced into 3:2 by dividing with 5

and 9:6 can be reduced to 3:2 by dividing with 3

keep smiling.

Answer:

D

Step-by-step explanation:

just got in edg 2021

Please Help ASAP will give a brainliest the questions are in the photos
{HELP WITH MATH}

Answers

Answer:

its should almost be certainly be A

Step-by-step explanation:

Jeanette obtained 32% for her statistics test, which was out of a total of 300 marks. How much should she score in the computer science test that is out of 200 marks in total if she is to get a proportionally weighted average of 46%?

Answers

Using weighted average, it is found that she should score 67% on the computer science test.

The weighted average is given by each proportion multiplied by it's score.

In this problem, the proportions and scores are given by:

Proportion of 32% = 0.32 for a score of 300.Proportion of x for a score of 200.Proportion of 46% = 0.46 for a score of 300 + 200 = 500.

Then

[tex]0.32(300) + 200x = 0.46(500)[/tex]

[tex]200x = 0.46(500) - 0.32(300)[/tex]

[tex]200x = 134[/tex]

[tex]x = \frac{134}{200}[/tex]

[tex]x = 0.67[/tex]

She should score 67% on the computer science test.

A similar problem is given at https://brainly.com/question/24855677

Entrance to a state park costs $6 per vehicle, plus $2 per person in the vehicle the cost for a bus with 50 people?

Answers

Answer:

$106

Step-by-step explanation:

So, this is what we know:

$6 per vehicle (1 bus) + $2 per person (50 people)

Here is the solution:

= $6 + $100

= $106

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